Solve 120+1.96120/sqrt{50}

$$120 + 1.96 \frac { 120 } { \sqrt { 50 } }$$

Evaluate

$$\frac{588\sqrt{2}}{25}+120\approx 153.262302987$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$120+1.96\times \frac{120}{5\sqrt{2}}$$

Rationalize the denominator of \frac{120}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$120+1.96\times \frac{120\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$120+1.96\times \frac{120\sqrt{2}}{5\times 2}$$

Cancel out 2\times 5 in both numerator and denominator.

$$120+1.96\times 12\sqrt{2}$$

Multiply 1.96 and 12 to get 23.52.

$$120+23.52\sqrt{2}$$

Factor

$$\frac{12 {(49 \sqrt{2} + 250)}}{25} = 153.2623029870152$$